## Solutions to set-IV

In this page, 'Solutions to set-IV' we are discussing how to do the problems given in problems on set-IV.

### Union and intersection

The following problems are under union and intersection of sets.

1.Find A∪B and A∩B for the following sets.

(i)     A = {0, 1, 2, 4, 6} and B = { -3, -1,0, 2, 4 5}

Solution:

A∪B       =     {-3, -1, 0, 1,2, 4, 5, 6}

A∩B       =     { 0, 2, 4}

(ii)    A = { 2, 4, 6, 8}  and   B =  ∅

Solution:

A∪B      =      {2, 4, 6, 8}

A∩B      =       { }

(iii)   A = { x: xℕ, x  ≤ 5} and B = {x: x is a prime number less than 11}

Solution:

Let us first write the given sets in Roster form.

A         =     {1, 2, 3, 4, 5}

B         =     { 2, 3, 5, 7}

A∪B      =        {1, 2, 3, 4, 5, 7}

A∩B       =         {2, 3, 5}

(iv)  A= {x: xℕ, 2<x ≤ 7} and B ={x: x ∈ W, 0 ≤ x ≤ 6}

Solution:

A        =        { 3, 4, 5, 6, 7}

B       =         {0, 1, 2, 3, 4, 5,6}

A∪B      =           {0, 1, 2, 3, 4, 5, 6, 7}

A∩B      =           {3, 4, 5,6}

2.If       A= {x: x is a multiple of 5, x ≤ 30, xℕ}

B = {1, 3, 7, 10, 12, 15, 18, 25},

Find (i)A∪B and (ii) A∩B.

Solution:

Let us first write the set A in Roster form.

A         =       {5, 10, 15, 20, 25, 30}

B         =       {1, 3, 7, 10, 12, 15, 18, 25}

(i)   A∪B        =         {1, 3, 5, 7, 10, 12, 15, 18, 20, 25, 30}

(ii)   A∩B        =         {10, 15, 25}

3. If X = {x: x = 2n, x ≤ 30 and xℕ} and

Y  = {x: x = 4n, x  ≤ 20 and ∈ W}

Find (i) X∪Y  and (ii) X∩Y

Solution:

Let us first write the given sets in Roster form.

X       =     {2, 4, 6, 8,10,12, 14, 16, 18, 20, 22, 24, 26,28, 30}

Y       =     {0, 4, 8, 12, 16, 20}

(i) X∪Y       =        {0, 2, 4, 6, 8,10,12, 14, 16, 18, 20, 22, 24, 26,28, 30}

(ii)X∩Y       =         { 4, 8, 12, 16, 20}

4. U = {1, 2, 3, 6, 7, 12, 17,21, 35, 52, 56},

P = { numbers divisible by 7}, Q= {prime numbers},

List the elements of set {x: x∈P∩Q}

Solution:

U           =        {1, 2, 3, 6, 7, 12, 17,21, 35, 52, 56}

P           =         {7, 21, 35, 56}

Q          =         {2, 3, 7, 17}

P∩Q       =          {7}

The following problems are under disjoint sets.

5. State which of the following are disjoint sets.

(i)   A = { 2, 4, 6, 8}

B = {x: x is an even number less than 10,  x ∈ ℕ}

Solution:

A      =        { 2, 4, 6, 8}

B       =        {2, 4, 6, 8}

A and B are equal sets, so they are not disjoint.

(ii)    X  =  { 1, 3, 5,7, 9},    Y = {0, 2, 4, 6, 8, 10}

Solution:

X and Y are not having common elements, so they are disjoint sets.

(iii)   P  =  {x: x is a prime < 15}

Q  =  {x: x is a multiple of 2 and x < 16}

Solution:

P             =           {2, 3, 5, 7, 11, 13}

Q             =            {2, 4, 6, 8, 10, 12, 14}

P and Q are having one element common, so they are not disjoint sets.

(iv)   R =  {a, b, c, d, e},      S = {d, e, a, b, c}

Solution:

R  and S are equal sets. So they are not disjoint sets.

Parents and teachers can encourage the students to do the problems on their own and become master in union and intersection of sets.  If you have any doubt you can verify the solutions given in the above page 'Solutions to set-IV'. Still if you have any doubt you can contact us through mail, and we will help you to clear all your doubts.